Actually the reason why Lamia is pushing so hard for Uriel to become the successor is because their family has, on multiple occasions, petitioned to the King to find out who was behind the attack of Uriel and punish them with zero results. Everyone knows it's the second prince who hurt him but the king refuses to do anything so the only way the Orphea family can push the case through the courts and persecute the second prince is if Uriel inherits the position as Duke, because then his position will be much higher than a spare and will then be one of the pillars of the kingdom (the Orphea family is the only dukedom in the kingdom and controls the entire south). Which makes it way worse because that small chance of revenge is the whole reason why Lamia is giving up her position even though she clearly doesn't really want to.
I hate all of y'all who think they should just stop fighting and get together just because this is a romance story. Y all the same people to eat up that killing stalking manhwa aren't you? Weirdos. He fucked up uri's hand FOR LIFE. Thats not just something to brush off your shoulder. The second Prince switches up whenever he feels like it so he isn't exactly that trustworthy. The only stupid thing lamia has dome so far is insist that uri be the successor when their roles are so obviously clear in the family...